Equivalent Definitions of A Closed Set
In a topological space, a set is closed if and only if it coincides with its closure. Equivalently, a set is closed if and only if it contains all of its limit points.
This is not to be confused with a closed manifold.
Read more about this topic: Closed Set
Famous quotes containing the words equivalent, definitions, closed and/or set:
“For some men the power to destroy life becomes the equivalent to the female power to create life.”
—Myriam Miedzian, U.S. author. Boys Will Be Boys, ch. 4 (1991)
“What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
—G.C. (Georg Christoph)
“A closed mouth catches no flies.”
—Miguel De Cervantes (1547–1616)
“There is one thing that matters—to set a chime of words tinkling in the minds of a few fastidious people.”
—Logan Pearsall Smith (1865–1946)